More than three times as many Massachusetts Democrats would vote for Hillary Clinton if she ran for president in 2016 than would back the state’s senior senator, Elizabeth Warren, according to a poll released Monday by Suffolk University and The Boston Herald.

Clinton, the former secretary of state and first lady, would garner 55 percent of the vote among 400 Massachusetts Democrats likely to vote in next month’s gubernatorial primary, while Warren -- who has repeatedly said that she is not running for president -- would curry 17.25 percent. Vice President Joe Biden drew just 7.75 percent of the vote. Warren would be the second choice of 27 percent of those polled, while Biden would get almost 24 percent of the back-up vote.

Warren unseated former Republican senator Scott Brown in 2012, with a winning margin of 8 percentage points. On the same ballot, President Obama beat Mitt Romney, the state’s former governor, by 23 percentage points. Warren has disavowed on multiple occasions interest in running for president, but has not foreclosed entirely on the option.

The same poll shows Attorney General Martha Coakley leading the gubernatorial primary with more than 42 percent of the vote, with Treasurer Steve Grossman at 30 percent -- portraying a race significantly closer than a series of public polls have showed. Coakley advisers have acknowledged they expect the race to tighten as the Sept. 9 primary draws near and Grossman’s on-air presence has outpaced Coakley’s.

Get Fast Forward in your inbox:

Forget yesterday's news. Get what you need today in this early-morning email.

Former federal health care administrator Don Berwick drew 16 percent of the vote. More than 11 percent of voters were undecided. Asked how they would vote if their preferred candidate loses in the primary, 26 percent of voters said they were undecided, while 60 percent said they would back the Democratic nominee.

The Suffolk/Herald poll also quizzed 400 Republicans likely to vote in the GOP primary. More than 70 percent said they planned to vote for venture capitalist Charlie Baker over Tea Party-affiliated Mark Fisher, who slightly more than 11 percent of the vote.